A digital elevation model (DEM) is a digital file consisting of a sampled array of terrain elevations for ground positions at regularly spaced horizontal intervals. Thus, a DEM is the topographic data composed of the set of horizontal coordinates (x, y) and its elevation (z) for each grid cell in a given region. Building a DEM is done in three steps: (1) an image-matching step to find overlapped regions from stereo images, (2) a camera-modeling step to obtain coordinates (x,y,z) from the results of the image-match using a camera model that relates the photo plane with absolute ground coordinates, and (3) an interpolation step to change the uneven horizontal distribution resulting from the camera model into a uniform horizontal square distribution (cells).
The USGS Digital Elevation Model (DEM) data files are digital representations of cartographic information in a raster form. The USGS produces five different digital elevation products. Although all are identical in the manner the data are structured, each varies in sampling interval, geographic reference system, areas of coverage, and accuracy. The primary differing characteristic is the spacing, or sampling interval, of the data.
DEMs may be used in the generation of three-dimensional graphics displaying terrain slope, aspect (direction of slope), and terrain profiles between selected points. At the USGS, DEMs have been used in combination with digital raster graphics (DRGs), digital line graphs (DLGs), and digital orthophoto quadrangles (DOQs) to both enhance the visual information for data extraction and revision purposes and to create aesthetically pleasing and dramatic hybrid digital images. Non-graphic applications such as modeling terrain and gravity data for use in the search for energy resources, calculating the volume of proposed reservoirs, and determining landslide probability have also been developed.
A DEM file is organized into a series of three records, A, B, and C. The A record contains information defining the general characteristics of the DEM, including its name, boundaries, units of measurement, minimum and maximum elevations, number of B records, and projection parameters. Each B record consists of an elevation profile with associated header information, and the C record contains accuracy data. Each file contains a single A and C record, while there is a separate B record for each elevation profile. More detailed information about the organization of a DEM file can be found in the National Mapping Program Technical Instructions, Standards for Digital Elevation Models and Digital Elevations Models: Data User's Guide.
The USGS plans to convert its DEM products to the Spatial Data Transfer Standard (SDTS) format. SDTS offers a mechanism for transferring data between dissimilar computer systems and offers the advantages of flexibility, improved quality, and no loss of information. It is the transfer mechanism for all Federal agencies.
These digital cartographic/geographic data files are produced by the U.S. Geological Survey (USGS) as part of the National Mapping Program. Currently, any Geographic Information System (GIS) supports Digital Elevation Model (DEM) data only as a 2-D system. DEMs may be projected using only 2-D horizontal datums (x, y), i.e., a GIS does not support vertical (z) datums (orthometric height) and geoid models used to derive them. Additionally, various datums may be derived from different ellipsoid and geoid models.
Point and vector positioning using GPS provides height data as a perpendicular distance from a reference ellipsoid, e.g., the WGS84 ellipsoid. However, elevation is measured by perpendicular distance from a geoid (a proxy for sea level) above a local datum that may comprise coordinates for locations that have been surveyed.
A body rotating with the Earth experiences its gravitational attraction (and that of other celestial bodies) and a centrifugal force due to Earth's rotation about its axis. This produces a gravitational force vector g(x,y,z) that may be described as a sum of a gravitational field and a centrifugal potential field. This sum defines a set of equipotential surfaces, defined by:W(x,y,z)=a constant  (1)on each of which surfaces the magnitude of the vector, g, is constant. Each of these equipotential surfaces is known as a geoid. A. Leick, GPS Satellite Surveying, John Wiley & Sons, New York, Second Edition, 1995, pp. 215–232. Because the local gravitational attraction will differ for a location near a mountain range and a location with no topographic relief, a geoid surface is not smooth everywhere and has bumps or undulations.
Real-time kinematic (RTK) GPS allows one to determine a set of parameters that relate measured or stored WGS84 heights above the ellipsoid to local control elevations, or benchmarks. This models the relationship between the local vertical datum and the ellipsoid as an inclined plane with parameters that describe the location and orientation of a best fitting plane.
To determine the precise range from an Earth-based receiver to a satellite, a reference coordinate system is chosen such that the instantaneous location of the satellite and the receiver are expressed in a uniform coordinate system. GPS uses a Cartesian, Earth-centered, Earth-fixed, coordinate system in which the positive x-axis points in the direction of 0° latitude, the positive y-axis points in the direction of 90° east longitude, and the resultant xy-plane defines Earth's equatorial plane. To transform Cartesian coordinates into the latitude, longitude and height coordinates of the receiver, a physical model of Earth is adopted. This model is based on an oblate ellipsoid having a semi-major axis length, a, and a semi-minor axis length, b, with b≦a. The values for the lengths a and b are chosen to most nearly match a mean sea level, or geoid, surface. One such ellipsoid is the WGS84 ellipsoid. Leick, p. 487. Other ellipsoids include the Bessel 1841, Clarke 1880, International 1924, Krassowsky 1940, and GRS80 ellipsoids. In some instances, a “local” ellipsoid that better matches a local region is used in place of the WGS84 or other global ellipsoid.
Local or global geodetic coordinates are sufficient to define horizontal coordinates. However, vertical coordinates are referenced to a geoid vice an ellipsoid. By definition, the ellipsoid has a smooth shape. The shape of the selected geoid is influenced by the mass distribution in the Earth, and by the resulting local gravity gradient and any variations therein. In regions where the distribution of mass is homogeneous and the gravity variation is negligible, the difference between the geoid surface and the ellipsoid surface may be adequately represented by a vertical offset, normal to the ellipsoid surface. In regions where the gravity variation is non-negligible but constant, the difference between the geoid surface and the ellipsoid surface is better represented by a selected vertical offset and selected tilt angles along two orthogonal axes, i.e., a vertical plane adjustment. However, in regions where the distribution of the Earth's mass is non-homogeneous or where survey measurements are performed over large spatial distances, large fluctuation in the gravity gradients can occur, and the planar model relating height relative to the geoid and the ellipsoid degrades in accuracy. For example, on the plains of Kansas, a planar model might be sufficient for a 10,000 kilometer2 (Km2) project area, whereas at the foot of the Rocky Mountains a planar model may provide only a good approximation on a 10 Km2 project area. For this reason, different models may be deemed appropriate for use as DEMs for even small areas of interest.
A number of patents address data fusion problems related to topography, some of which may be useful as inputs to a process representing a preferred embodiment of the present invention. Among these are:
U.S. Pat. No. 4,899,293, Method of Storage and Retrieval of Digital Map Data Based Upon a Tessellated Geoid System, to Dawson et al., Feb. 6, 1990, incorporated herein by reference. The '293 patent provides a method for storage and retrieval of digital map data representative of a tessellated sphere.
U.S. Pat. No. 5,729,451, Apparatus and Method for Fusing Diverse Data, to Gibbs et al., Mar. 17, 1998, incorporated herein by reference. The '451 patent describes an improved data fusion station that may have a number of uses including geo-technical engineering.
U.S. Pat. No. 5,652,717, Apparatus and Method for Collecting, Analyzing and Presenting Geographical Information, to Miller et al., Jul. 29, 1997, incorporated herein by reference. The '717 patent provides a process for manipulating geographic information from a variety of sources on a generic GIS.
U.S. Pat. No. 5,675,407, Color Ranging Method for High Speed Low-Cost Three Dimensional Surface Profile Measurement, to Geng, Oct. 7, 1997, incorporated herein by reference. The '407 patent uses a unique “color ranging” method to depict and manipulate elevation data.
U.S. Pat. No. 5,923,278, Global Phase Unwrapping of Interferograms, to Poehler et al., Jul. 13, 1999, incorporated herein by reference. The '278 patent provides a unique process for unwrapping a wrapped phased array data set representative of an interferogram.
U.S. Pat. No. 5,926,581, System for Topographic Mapping from Remotely Sensed Images, to Pritt, Jul. 20, 1999, incorporated herein by reference. The '581 patent employs images of terrain generated at different angles to supply matching points that are then used to develop coefficients of a coefficient mapping equation. A height term of the equation is corrected into an elevation term in the coordinates of one of the images. The elevation is then rotated into the coordinates of the ground plane of the terrain to result in a DEM.
U.S. Pat. No. 6,016,118, Real Time Integration of a Geoid Model into Surveying Activities, to Jackson et al., Jan. 18, 2000, incorporated herein by reference. The '118 patent enhances the elevation accuracy from a GPS-developed survey through use of an optimal locally-best-fitting plane combined with a local geoid model.
U.S. Pat. No. 6,424,287 B1, Error Correction for IFSAR, to Doerry et al., Jul. 23, 2002, incorporated herein by reference. The '287 patent improves elevation estimates by compensating for variations in vertical separation between antenna collection surfaces by adjusting the baseline projection during image projection.
Conventionally, any transformation of the horizontal and vertical datums of differing sources is handled manually. By employing any raster-based GIS, a process is needed to accurately and automatically merge into a “new merged” DEM two or more different DEMs based in different vertical datums (and possibly different horizontal datums) from various ellipsoid and geoid models. It is also preferable that the process automatically provides, as a decision design, software checking routines for both horizontal and vertical datums as well as for any geoid models used. A preferred embodiment of the present invention does this, yielding true 3-D objects in a 3-D environment.